Article
Mathematics, Applied
Hoang Hai Ha, Ky Ho, Inbo Sim
Summary: The paper investigates the existence of infinitely many solutions for a generalized p-Laplace equation involving Leray-Lions operators. Different conditions on the nonlinear term lead to properties of the solutions, such as approaching 0 or the divergence of Sobolev norms to infinity.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Khaled Kefi, Dusan D. Repovs, Kamel Saoudi
Summary: This study investigates the existence and multiplicity of weak solutions for fourth-order problems involving Leray-Lions type operators in variable exponent spaces, and improves a result from Bonanno and Chinn (2011) by applying variational methods and a multiplicity theorem from Bonanno and Marano (2010).
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Jian Liu, Zengqin Zhao
Summary: In this article, we investigate p(x)-biharmonic equations involving Leray-Lions type operators and Hardy potentials. Some new theorems regarding the existence of generalized solutions are reestablished for such equations when the Leray-Lions type operator and the nonlinearity satisfy suitable hypotheses in variable exponent Lebesgue spaces.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Z. Musbah, A. Razani
Summary: This paper studies the existence of multiple solutions to a nonlocal system involving fourth order Leray-Lions type operators along with singular terms under Navier boundary conditions, using variational methods.
BOUNDARY VALUE PROBLEMS
(2022)
Article
Mathematics, Applied
Yun-Ho Kim
Summary: This paper aims to derive multiple multiplicity results of nontrivial weak solutions to Kirchhoff-Schrocenter dotdinger equations involving the p(center dot)-Laplace-type operator. It shows the existence of infinitely many large energy solutions and small energy solutions under certain conditions on the nonlinear term. The fountain theorem and the dual fountain theorem are the primary tools used to obtain these multiplicity results.
Article
Mathematics
K. Kefi, N. Irzi, M. Mosa Al-shomrani
Summary: This paper establishes the existence of at least three weak solutions for the fourth-order problem with indefinite weights involving the Leray-Lions operator with nonstandard growth conditions. The result obtained by Kefi et al. is generalized, and the proof of the main result relies on variational methods and the critical theorem of Bonanno and Marano.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
(2023)
Article
Mathematics
K. Kefi, N. Irzi, M. M. Al-Shomrani, D. D. Repovs
Summary: This article proves the existence of at least three weak solutions for the fourth-order problem with indefinite weight involving the Leray-Lions operator with nonstandard growth conditions.
BULLETIN OF MATHEMATICAL SCIENCES
(2022)
Article
Mathematics, Applied
Hammad Nafis, Humberto Rafeiro, Muhammad Asad Zaighum
Summary: This paper proves the boundedness of multilinear Calderon-Zygmund operators on the product of grand variable Herz spaces, which generalizes the boundedness of these operators on the product of variable exponent Lebesgue spaces and variable Herz spaces.
JOURNAL OF FUNCTION SPACES
(2022)
Article
Mathematics, Applied
Aigerim Kalybay
Summary: This paper investigates the boundedness of a certain class of Hardy operators with kernels from a second order weighted Sobolev space to a weighted Lebesgue space.
JOURNAL OF FUNCTION SPACES
(2022)
Article
Mathematics, Applied
Shuhui Yang, Yan Lin
Summary: This paper investigates the boundedness properties of a class of multilinear strongly singular integral operators on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces. Additionally, the authors obtain endpoint estimates for L(infinity)x -> BMO and BMO x -> BMO.
Article
Mathematics
Esra Kaya
Summary: This paper investigates the B-maximal operator on variable exponent Lebesgue spaces and establishes a necessary condition for its boundedness. It is proven that the B-maximal operator is unbounded when p(-) = 1, while the boundedness of the fractional maximal function associated with the Laplace-Bessel differential operator on the same space is demonstrated.
Article
Mathematics, Applied
Hussein Mesmar
Summary: This article investigates the existence of G-invariant positive solutions u: M → R to the nonlinear equation UDelta_gu + au = u^2i(k e)-1 d(x, Gx0) + huq-1 on the Riemannian manifold (M, g) with a group G of isometries. The authors prove existence using the Aubin minimization and the Mountain-Pass lemma of Ambrosetti-Rabinowitz. Additionally, they find the value of the best-constant in the associated Hardy-Sobolev inequality.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Lauren M. M. Bonaldo, Elard J. Hurtado, Olimpio H. Miyagaki
Summary: In this paper, the existence and multiplicity of weak solutions for a general class of elliptic equations with variable exponents and Dirichlet boundary conditions are studied. By using different versions of the Mountain Pass Theorem, as well as the Fountain Theorem and Dual Fountain Theorem, the existence of weak solutions for the problem is obtained. It is shown that there is at least one nontrivial solution for small parameter lambda > 0, and the solution blows up in the fractional Sobolev norm as lambda approaches 0. Moreover, the paper also proves the existence of infinitely many weak solutions that tend to zero in the fractional Sobolev norm for any parameter lambda > 0, under additional assumptions on the nonlinearity function.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2022)
Article
Mathematics, Applied
Yanqi Yang, Shuangping Tao, Guanghui Lu
Summary: In this paper, the authors investigate the commutators of bilinear pseudo-differential operators and the multiplication operation by a Lipschitz function. By establishing pointwise estimates of the corresponding sharp maximal function, the boundedness of the commutators is obtained on weighted Lebesgue spaces and variable exponent Lebesgue spaces. The authors also establish the endpoint estimate of the commutators on L-infinity x L-infinity.
Article
Mathematics, Applied
Shuhai Zhu
Summary: In this study, we investigate a Schrodinger type equation with variable exponents and a nonlinearity that is superlinear but does not satisfy the Ambrosetti-Rabinowitz type condition. By applying variational techniques and the fountain theorem, we establish the existence and multiplicity of nontrivial solutions. Additionally, we demonstrate the existence of a sequence of solutions with high energies.
Article
Mathematics, Applied
Nikolaos S. Papageorgiou, Dusan D. Repovs, Calogero Vetro
Summary: In this paper, we consider an anisotropic (p,2)-equation with a parametric and superlinear reaction term. We prove that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, four with constant sign and the fifth nodal (sign-changing). The proofs employ tools from critical point theory, truncation and comparison techniques, and critical groups.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics
Dusan D. Repovs, Kamel Saoudi
Summary: This study investigates a singular problem involving the p(x)-Laplace operator, and applies the Nehari manifold approach and new techniques to establish the multiplicity of positive solutions for the problem.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
(2023)
Article
Mathematics, Applied
Abdeljabbar Ghanmi, Mouna Kratou, Kamel Saoudi, Dusan D. Repovs
Summary: The objective of this paper is to investigate a nonlocal problem involving singular and critical nonlinearities and explore the existence and multiplicity of positive solutions. By combining variational techniques with a truncation argument, the authors have obtained the desired results.
ASYMPTOTIC ANALYSIS
(2023)
Article
Mathematics
Zhongyi Zhang, Dusan D. Repovs
Summary: This paper studies the existence and multiplicity of solutions for degenerate fractional Schrodinger-Kirchhoff-Poisson equations with critical nonlinearity and electromagnetic fields.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
(2023)
Article
Mathematics
Shiqi Li, Sihua Liang, Dusan D. Repovs
Summary: This paper establishes the existence of solutions for critical exponential Kirchhoff systems on the Heisenberg group using the variational method. The novelty of this paper lies in considering the degenerate case for both the nonlinear term with critical exponential growth and the Kirchhoff function, and our result is new even for the Euclidean case.
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
(2023)
Article
Mathematics
Dusan D. Repovs, Mikhail Zaicev
Summary: This article studies polynomial identities of algebras with involution of nonassociative algebras over a field of characteristic zero. It is proven that the growth of the sequence of *-codimensions of a finite-dimensional algebra is exponentially bounded. A series of finite-dimensional algebras with fractional *-PI-exponent is constructed. Additionally, a family of infinite-dimensional algebras C alpha is constructed such that exp*(C alpha) does not exist.
JOURNAL OF ALGEBRA
(2023)
Article
Mathematics, Applied
Debajyoti Choudhuri, Dusan D. Repovs
Summary: In this paper, we establish the existence of a solution to a semilinear equation with free boundary conditions on stratified Lie groups. In the process, we prove a monotonicity condition that is essential for establishing the regularity of the solution.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Friedrich Hegenbarth, Dusan D. Repovs
Summary: We use the Gromov-Hausdorff metric dG to characterize certain generalized manifolds. We prove that generalized n-manifolds can be obtained by gluing two topological n-manifolds using a controlled homotopy equivalence. Moreover, we show that manifold-like generalized n-manifolds are limits of topological n-manifolds, and if these topological n-manifolds satisfy a certain local contractibility condition, the generalized n-manifold is resolvable.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Debajyoti Choudhuri, Dusan D. Repovs, Kamel Saoudi
Summary: In this paper, we prove the existence of solutions to a double phase problem with a nonlinear boundary condition. The novelty of our work lies in using the well known weak convergence method to guarantee the existence of solutions, which has not been studied before. We also provide an illustrative example.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2023)
Article
Mathematics
Nikolaos S. Papageorgiou, Vicentiu D. Radulescu, Dusan D. Repovs
Summary: This paper studies a Neumann boundary value problem driven by the anisotropic (p, q)-Laplacian plus a parametric potential term. The reaction exhibits superlinear behavior. The paper proves a global multiplicity result for positive solutions with respect to the parameter. Additionally, the existence of a minimal positive solution is shown, and a nodal solution is produced.
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS
(2023)
Article
Mathematics, Applied
Debajyoti Choudhuri, Dusan D. Repovs
Summary: We establish the existence of at least two solutions for the Prandtl-Batchelor elliptic problem with a power nonlinearity and a singular term by utilizing a series of C-1 functionals and a cutoff function. Due to the nondifferentiability of the associated energy functional, traditional variational techniques are ineffective. Our approach involves fundamental elliptic regularity theory and the mountain pass theorem as the main tools.
BOUNDARY VALUE PROBLEMS
(2023)
Article
Mathematics, Applied
Nabil Chems Eddine, Dusan D. Repovs
Summary: This paper deals with the Neumann problem for a class of quasilinear stationary Kirchhoff-type potential systems, which involve elliptic operators with variable exponents and real positive parameter. By combining the truncation technique, variational method, and the concentration-compactness principle for variable exponent under suitable assumptions on the nonlinearities, we prove the existence of at least one solution of the problem, which converges to zero in the norm of the space as the real positive parameter tends to infinity.
BOUNDARY VALUE PROBLEMS
(2023)
Article
Mathematics, Applied
Yueqiang Song, Yuanyuan Huo, Dusan D. Repovs
Summary: We study a class of Schrodinger-Poisson systems with (p, q)-Laplacian and obtain a new existence result for nontrivial solutions using fixed point theory. The main novelty of the paper lies in the combination of a double phase operator and the nonlocal term. Our results generalize some known results.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics
Maurizio Imbesi, Giovanni molica Bisci, Dusan D. Repovs
Summary: In this paper, we study the existence of classical solutions for a class of elliptic equations involving the mu-Laplacian operator on a weighted graph G. By using direct variational methods and applying key conditions, we are able to prove the existence of at least two solutions for the studied problems. Our results improve upon previous research.
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS
(2023)
Article
Mathematics, Applied
Soraya Fareh, Kamel Akrout, Abdeljabbar Ghanmi, Dusan D. Repovs
Summary: In this article, the authors investigate certain critical Schrodinger-Kirchhoff-type systems with the fractional p-Laplace operator on a bounded domain. By utilizing properties of the functional energy on the Nehari manifold sets and analyzing the fibering map, the authors establish the multiplicity of solutions for such systems.
ADVANCES IN NONLINEAR ANALYSIS
(2023)
